2-extendability and k-resonance of non-bipartite Klein-bottle polyhexes

Qiuli Li, Saihua Liu, Heping Zhang
2011 Discrete Applied Mathematics  
C. Thomassen classified Klein-bottle polyhexes into five classes [C. Thomassen, Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface, Trans. Amer. Math. Soc. 323 (1991) 605-635 ]. In this paper, by implementing cutting and gluing operations, we reclassify the five classes of Klein-bottle polyhexes into two classes-the bipartite case K (p, q, t) and the non-bipartite case N(p, q, t). Further, we completely characterize 2-extendable and k-resonant non-bipartite Klein-bottle polyhexes, respectively.
doi:10.1016/j.dam.2010.12.015 fatcat:pptg36upljgdfiafdi2rrwmagu